This guide's purpose is to try to give beginners a kick start into a fast method of solving the Rubik's cube. It is not intended to be easy in any way, and it probably won't be. By following this guide, you leave open much more space for improvement than with slow, tedious beginner methods. At some points, you may feel like giving up. All I can tell you is that if you do follow the guide through, it will pay off in the end.

Good luck.
-Trevor "tj9991" Slocum

Intuitive F2L (First Two Layers)

First, get a cross on the bottom of your cube:


Then, pair a corner and an edge together. These are correctly paired corners and edges:
 

In order to pair corners and edges, you will need to be able to know how to move and orient them in a way you can place them together.
The following are the fundamental positions and moves for pairing a corner with an edge.
 

While intuitive F2L is all about discovering how to deal with situations without using algorithms, here are a few examples to get you started:
   

Orienting the Last Layer

When you have all of the first two layers completed, you must then orient the last layer.
Warning!
The rest of the guide requires that you know the standard Rubik's cube notation!
If you are unsure if you know it well enough to read the algorithms below, I have wrote a short and to-the-point guide here.

The Cross

First, we make a cross, almost like we did in the very beginning.
I want you to only focus on the edges and center stickers of the last layer.
You will have one of three conditions:
FRU R'U'F'FUR U'R'F'FUR U'R'F' U FRU R'U'F'
OR
FRU R'U'F' U2 FUR U'R'F'
In the third case, you can pick either, since they will do the same operation. I prefer the first one, but it's up to you.
Once you are done with one of the three cases, your top layer will look something like this:


For the next three steps, I have a printable page to help with memorization, which you can take anywhere. It is available here.

Orienting the Corners

Now that your edges face up with the correct color, we need to get the corners to do the same.
We do this by memorizing two different algorithms.
[A]     [A]-1
R'U2RUR'UR     R'U'RU'R'U2R
We then memorize the seven cases which can occur on the last layer.
[A][A]-1
  
[A][A][A] U [A]
  
[A] U [A]-1[A] U2 [A]-1
  
 
[A] U' [A]-1 
If your last layer doesn't match any of the cases, then you either need to turn it until it looks like one, or dissassemble your cube, because theyre not in properly.

Permuting the Last Layer

Permuting the last layer is actually moving the corners and edges into their proper places.
There are only two algorithms you need to memorize for permuting the corners, and two algorithms you need to memorize for permuting the edges.

Permuting the Corners

The following are the two algorithms you need to know for moving three corners clockwise and counter clockwise.
     
x (R'UR') D2 (RU'R') D2 R2 x'     x R2 D2 (RUR') D2 (RU'R) x'
       
     
It will take some time to be able to identify which needs to be used and where, so don't get frustrated if you don't get it right away :)

Permuting the Edges

The following are the two algorithms you need to know for moving three edges clockwise and counter clockwise.
     
(R2' U)(R U R' U')(R' U')(R' U R')     (R U')(R U)(R U)(R U')(R' U' R2)
       
     

Solved!

Congratulations, you've just solved the Rubik's cube!